Wednesday, February 28, 2007

Who to Believe: Auto Speed and Accident Mortality

In a recent Usenet exchange, a poster informed me that "The studies show that if you hit a pedestrian at 20mph there is a 95% survival rate, at 30mph it is 80%, at 40mph it is 10% (or 20% for a small child)." I found the size of the effect implausibly large, asked for a source, and was told that it was "A paper by Ashton and Mackay."

Curious, I turned to Google. The facts, so far as I can determine them:

The paper is cited as Aston and Mackay (1979). Many references give what appear to be the same figures, cited to a U.K. dept of Transport publication from 1992; my guess is that it's citing the paper. One webbed source gives the figures as:

"A pedestrian has a 95 per cent survival rate when hit by a car driving at less than 20mph. At less than 30mph their survival rate is 55 per cent. At 40mph, survival rates are only 5 per cent. (Ashton and Mackay 1979)"

In this version the figure is not for 20 mph but for "less than 20 mph," averaging in the collisions at five or ten miles an hour, and similarly for "less than 30 mph." Comparing "less than 30 mph" to "At 40 mph" makes the difference between 30 and 40 look a lot larger than it actually is. On the other hand, some other pages citing the figures give them as "20 mph," "30 mph," "40 mph"—with the same survival rates. The poster also strikingly exaggerated the survival rate associated with 30 mph, but that's not terribly surprising since he, like the earlier poster whose information he was attempting to clarify, was presumably working from memory. I gather the figures have been extensively used in the U.K. in attempts to persuade drivers to drive more slowly.

Which gets me to the real point of this post. Googling around, it seemed clear that the figures are routinely used by people who want to persuade other people to drive more slowly, hence people with an obvious interest in claiming that mortality rates increase rapidly with speed. I conclude that the "under 30 mph" version is probably the real one, since converting that to "at 30 mph" makes the argument look stronger. I also note that the figures are from research done nearly thirty years ago, which is at least mildly suspicious; it suggests that the people quoting those figures, with no explanation of how they were calculated, may be selecting the study that best supports what they want others to believe, not the most recent or best study. I have not been able to find any webbed version of the study itself; if a reader has actually seen it, I would be interested to know just how the figures were calculated.

Finally, I did come across one interesting bit of actual data relevant to the question:

"in Zurich, the urban area speed limit was lowered from 60 to 50 km/h [37 to 31 mph] in 1980 ... . In the year after the change in the urban speed limit there was a reduction of 16 percent in pedestrian accidents and a reduction of 25 percent in pedestrian fatalities (Walz et al, 1983)."

That implies that fatalities/accident, the relevant figure for calculating the survival rate, fell by only about 9% when maximum speed went from 37 to 31 mph. It's hard to see how that can be consistent with the sort of drastic reduction of mortality that is supposed to be associated with speed reduction within the same range according the figures attributed to the Ashton and Mackay paper.

When deciding whether to believe what someone says, it is worth first asking why he is saying it and how strong his incentives are to know whether it is true. Readers who have hard data on either side of the question are invited to submit it. Why should I do all the work?


After writing the above, I discovered that another Usenet poster, better at using Google than I am, has tracked down what appears to be the original paper. It contains no numbers corresponding to those cited, only a couple of figures with hand drawn graphs, one showing the frequency and one the cumulative frequency of various levels of injury as a function of speed. Trying to estimate numbers from the graphs on Figure 1, the survival rate if hit at 30 mph appears to be about 75%, at 40 mph between 20% and zero—the latter figure is very uncertain since at that point the width of the line is a significant fraction of its height above the axis.

Looking at the cumulative distribution (Figure 2), it appears that it is indeed the source for the 30 mph figure, since the ratio of fatalities to all injuries is about 45%, implying a survival rate of about 55%. So it looks as though the comparison being made is between the survival rate at under 30mph and the rate at exactly 40 mph, as I conjectured.

There is, however, a small problem. The first graph shows a considerably higher survival rate at 30 than the second shows at under thirty; since survival rates are falling as speed increases, that is impossible. Either I have misread the graphs—readers are invited to explain how—or the paper all of these numbers are supposed to be based on gives results that are striking inconsistent, indeed impossibly so.

In looking at the graphs, note that speeds are given in kph not mph.


Anonymous said...

Well, I believe that the figures for less then 20mph are very scarce compared to fatal run-overs with cars that were over 30 or 40mph. Also I would like to know if any of the accidents used to create the number had other factors that maybe influenced the deadly outcome (where the person landed, average age of the victims, other health conditions that agravated the situation) and many other variables that make this kind of study hard to take in consideration unless you have that data to take the conclusions from.


Anonymous said...

"since survival rates are falling as speed increases, that is impossible"

Could very well be a statistical anomoly due to lower number of < 20mph accidents reported. Indeed many < 20mph pedestrian accidents may simply go unreported as the person is unharmed or only midly bruised.

However, the assumption that survival rate decreases with speed may not hold true for all speed ranges.

For example, I would suspect that < 20mph accidents may involve a higher percentage of "large slow moving visibility-impaired vehicles" such as buses, trailers, heavy trucks, etc; that obviously pose more harm risk than brushing the bumber of a passenger car.

Furthermore, at 30mph you are probably more likely to "bounce" out of harms way than at <20mph, where you may find yourself under the vehicle in question.

David Friedman said...

"However, the assumption that survival rate decreases with speed may not hold true for all speed ranges."

Whether it's true of the real world I don't know, although it seems plausible. But it appears to be true of the graphs in the paper, which is the relevant question here.

So far as the issues gus raised, the paper did discuss other factors but it made no attempt to control for them in its graphs for the effect of speed. And it didn't give any description of its data set beyond the source--in particular, didn't say what the basis was for estimating the speed of the vehicle that caused the injury.

Anonymous said...

Yeah, my skeptcism about the paper comes more from the data than from the conclusions. Isn't it possible that many of the victims that see the car coming had heart attacks and THAT killed them? Well, I think a new study about this is needed, anything that has not been researched since 1979 deserves a new look.


Anonymous said...

This is a bit offtopic but kinda fits into your "who to believe" stories and the improper use of studies:

A recent study in Germany, "Does Money buy higher schooling?" (, has found that once you use an appropriate approach (sibling fixed effects, natural experiments), there is no evidence that a the income of parents has an influence on secondary schooling achievements of children. The first part of the study, however, explains the problems that come with a straightforward approach. Simply looking at descriptive statiscts and not accounting for unobserved heterogeneity "shows" that higher parental income does "buy" higher schooling for the children.

Germany's leftist newspaper "die tageszeitung" cited that study. Guess which part they focused on. Guess which part they didn't mention.

Leonard said...

Google racing!

Here's data from the Feds on pedestrian death rates by speed (among other stats). They discuss it right and left. In any case, there's some data from Florida in figure 1 that appears to be pretty solid.

Also have a look at table 10. It shows just what you want: the distribution of pedestrian fatalities across travel speeds. Numbers are as follows:

Speed Fatality%
0-20 8.2
21-25 5.3
26-30 9.7
31-35 14.6
36-45 28.5
46+ 33.6

Leonard said...

One important thing to note about fatalities of almost any kind is that fatality rates have dropped steadily over the years. This is not just in car/person accidents, but in car accidents generally, gunshot wounds, falls, etc.

Presumably this is due to better medical care and better medical transport. In the case of car/pedestrian encounters, it may also be because we are designing safer intersections or safer cars, or some such.

Looking at data that's more than 10 years old is pretty worthless, at least without trying to account for these effects.

Anonymous said...

Reminds me of an article in the Skeptic from a couple of years ago:
The ten percent solution: anatomy of an education myth.
Volume 10, Number 4

FOR MANY YEARS, VERSIONS OF A CLAIM that students remember "10% of what they read, 20% of what they hear, 30% of what they see, 50% of what they see and hear, and 90% of what they do" have been widely circulated among educators. The source of this claim, however, is unknown and its validity is questionable. It is an educational urban legend that suggests a willingness to accept assertions about instructional strategies without empirical support.

Anonymous said...

I guess the NHTSA study clears a lot up, but I'm curious how much of an impact (literally and statistically) the weight of the vehicle has, since heavier vehicles have more energy than lighter vehicles at the same speed. (I'm guessing vehicles tended to be heavier in 1979.)

Anonymous said...

Another interesting thing I noticed about another public safety film is the video ( for the 'how close' commercial lies.

If you freeze the video on the first run throuhg the man looks and the road is 100% clear, no motorbike at all (the motorbike then crashes into his side)...The second run-through the motorbike is visible even before he looks, during his first look and then ultimtaely passes by as he watches.

The advert need not lie like this to get across what is a very valid point - look left, look right, look left again.

Anonymous said...

designing safer intersections

That could plausibly explain the low nhtsa numbers because they are about posted speed. Safer intersections could lead to drivers braking before striking the pedestrian. I am skeptical that safer intersections or cars protect pedestrians from a collision at a given speed. In particular cars are so much heavier than people that I find it unbelievable that their increasing weight makes a difference.

(OK, crumpling bumpers could protect pedestrians, but I don't think they've improved. Better designed intersections might convert direct hits to glancing blows, also.)

It seems hopeless to assess the speed of cars in accidents. Posted speed is a pretty good proxy. Speed typically traveled on the road is measurable and useful for policy.

Anonymous said...

One look at the front end of most cars designed and produced during the past three years or so - and if you will, one prod with a finger at the front "bumper" and bonnet - will show the "pedestrian-friendly" (ahem) design and structure now required by the EU. The car is supposed to scoop up the pedestrian, rolling them across a soft front panel and bonnet, and then at faster speeds, roll them up the windscreen so they can't be run over. Sounds horrendous, and I'd rather it wasn't me, but think back to the chromed bumpers and steel front panels of the 70's and 80's, and then wonder whether the speed / mortality figures should be updated!

Willi said...

The force of an impact between a moving body with high mass and a, more or less, stationary object with relatively low mass (the pedestrian) is proportional to the square of the velocity of the vehicle. It does not have anything (much) to do with the mass of the vehicle, only Of the pedestrian. That said, a better measure of the consequences is the exact positioning of the pedestrian relative to the vehicle. If it is a glancing blow that's one thing. If the pedestrian actually gets run over that's quite another thing.

David Friedman said...

Will writes:

"The force of an impact between a moving body with high mass and a, more or less, stationary object with relatively low mass (the pedestrian) is proportional to the square of the velocity of the vehicle."

Do you mean the maximum force? Force is instantaneous, and the momentum transfer occurs over time.

Assuming the collision is entirely inelastic, momentum transfer, which is the integral of force over time, is proportional to the velocity of the car. The time over which the transfer occurs should be inverse to the velocity. So maximum force should go as the square--but on the other hand, time over which that force is applied is inverse to velocity, and I'm not sure how the two interact in determining injury.

On another subject, someone online has persuaded me that I misread Figure 2. It's showing a cumulative not of fatalities as a number but of fatalities as a percent of total fatalities, so the scale is different for the different curves, so I can't just take their ratio.

I suspect, however, since my mistaken calculation gave the reported number, that I may not be the only one who made that mistake.

mulp said...

An inelastic collision, and in the case of a victim, the collision is ultimately completely inelastic, means that all the energy is dissipated in the victim. What is the energy? Well, the energy equal to the momentum of the victim traveling fast enough to not be hit by the car.

If the collision were elastic, the victim would keep bouncing, absorbing energy on each impact, and then releasing the energy absorbed when bouncing off.

A person is perfectly elastic, or nearly so, up to point, equal to a number of Gs, with the energy of deformation becoming heat at the molecular level which is then released as the deformation is relieved. However, exceed the elastic limit, and the heat tears the molecules apart: broken bone, torn flesh, etc.

Of course, if you are crossing the street in a city, and a car takes a turn and bumps you, perhaps even knocking you down, you most likely gesture at the driver, pick yourself up, continue on. How can any statistics capture that low speed collision having little to no injury?

But to your larger point, for me the most grating example of what you note here is the claim that the Club of Rome report, The Limits to Growth, have been proved totally false by history, citing various claims like "it said oil would run out by 1990 and it didn't happen, so it is totally wrong."

Aside from the facts that it was one of the earliest computer models, was reported as far from complete, was identifying a set of scarcities that would affect everything, including markets, with the intended effect being a change in behavior of everyone in anticipation of the changing scarcity, the book contained no dates, numbers, etc.

Obviously the [mis]representation of The Limits to Growth is intended to slant the argument in a particular direction.

For the most parts, the economy adapts to the limits to growth without major crisis or dramatic shifts in behavior or structure of society. The scarcity of space that population growth caused didn't result in people dying in droves, but it did result in a dramatic change in the nature of cities from relatively compact structures to massive sprawl.

Thinking about this at a more abstract level, and tying it to issues that I'm been trying to understand, I find it interesting that you looked at the physics problem and introduced time, and forces over time.

But economists, and the law to a lesser degree, ignore time as a factor in their theory or practice.

I got here from your website by way of wikipedia, stopping to read your paper where you talk of being in the field holding a spear with horsemen charging toward you, and you debate the choice of running vs standing.

The economist considers the situation and concludes from the non-time related cost-benefit analysis: run. Of course, the lack of time as a factor in the economist theory results in the fuzzy "short run" vs "medium run" vs "long run". In the short run, running is good, in the long run, running is bad.

The lawyer looks at things either from the standpoint, "it happened, what restores some sort of equity" or "'it' happening is unacceptable because true equity is impossible, so how do we prevent 'it' from happening."

The general, however, looks at the battle as a time dynamic part of a larger time dynamic system. He trains you to follow orders, and then he anticipates how you will react when standing in the field, how you will perform, and then sets the order of battle, sometimes calling for you to stand, sometimes to run, and sometimes to run and then stand, or stand then run.

Speed limits are imposed without taking the time dynamic into account - why not allow speeding at 3am, or why not an 80MPH speed limit at 3am, but only 10MPH at 3pm when school kids are going home?

The lawyer tends to see the kid getting killed as something to absolutely prevent. The economist sees the dead child and imprisoned driver as creative destruction (the driver and the child failed to successfully compete in the market place of space in the street ;-)

And the general is making decisions from the commanding heights, choosing who benefits, and who doesn't.

I think that we get all wrapped up in the details, forgetting the larger picture. As an engineer, I think I look at things as the general or politician: Yes, there are theories and such, and debates on the trade-offs, but I need to integrate many things into the decisions I make or recommend, being fully aware that over time, they will not result in the outcome predicted by the static analysis of the theorists.

And the theorists waste all their time debating the truth or falsity of the details without simply saying, here is what the theory says, it provides guidance, but not predictions of actual outcomes.

The Sanity Inspector said...

Google search tip: when you're looking for forms or official documents or research papers of this sort, and you're searching on the www instead of a periodical index, do the following: Go to Google and type in your search word or phrase, and add "filetype:pdf" This will return only pdf files, which are more likely to be the format in which the info you want is stored. This will also exclude most of the targeted advertising links that come up in html results.

montestruc said...

Also the mass of the vehicle is non-trivial. Usually one can assume the mass of the vehicle to be much larger, but in the UK in the 50's -70's the mean mass of the car is much less than modern day USA where trucks and SUVs are common.

Anonymous said...
This comment has been removed by a blog administrator.
Anonymous said...

"my guess is that it's citing the paper."
Ive heard a couple of people at my work say that, what does that mean? But I agree with anyone who says that the more accidents you have, the more expensive the rate goes up. But I've heard of a company who recently put a promotion that if you have a good record, then much lower rates and you get some sort of amount in money back in the end of the year

Jonathan Miller said...

I know this is 3 years old, but the answer to your question about the graphs being misleading is that they show the reverse of what people think they do.
They show all the fatal, serious and slight accidents in the given study, and then plot the speeds at which they occurred. The first set of distributions is a straightforward distribution curve showing how fast the car that caused a particular type of accident was traveling.
The second is the cumulative frequency of the speeds for each type of accident.
Although it is often assumed to be such, the graph is not showing survival rates at all, it just shows the speeds at which (e.g. fatal) accidents occur.

In the UK this paper is widely cited, despite it being 20 years out of date (cars are now routinely designed to be more pedestrian friendly). I think it is high time another study was done.

Dr. Ray Turner said...

I am researching school bus student pedestrian underride collisions and the types of injuries (fatal, non-fatal, what body parts, crush by rollover, etc.). If you calculate the Type C (conventional) school bus with a wheelbase of 21.56 feet travelling from 0 MPH in 7 seconds to 2.1 MPH or 3.08 fps the "speed" factor in pedestrian underride fatalities is almost irrelevant. What is very relevant is the First Harmful Event (FHE) at the front bumper (bumper base to ground=ground clearance in inches), then front axle ground clearance FHE2 (much lower than front bumper on most Type C school buses), then the FHE3 pedestrian body impact on the front tie rods, leaf springs, U-bolts, etc., then FHE4 (when tumbling after three consecutive collisions going at less than walking speed by the bus) the only window of survival for these students is a "roll out" from under the bus (96" wide/46" from undercarriage centerline). I have not been able to obtain accurate data on children's "rolling body speeds" from ages 4.5 yrs. to 19.5 yrs. I do know that in the 7 seconds from front wheel center to back wheel center took 7 seconds. I also know that the "roll out speed" required to move 48" (4 ft.) out from under the moving school bus is .58 fps or .57 MPH. Average speed for elementary child walking is 3.3 MPH. No one has done research on the rollout speed. Additionally, I know that many children wear backpacks which adds appx. 6" in chest depth (both sexes) to their underride strike zone or profile. I certainly think but cannot yet prove that rolling out with a backpack would significantly reduce their rollout speed and significantly increase their rear wheel crush at FHE5. Please note that the rear axle ground clearance is usually much lower than the front axle clearance (average 17" front axle and <12" for rear axle).
There is a new product to fit on the passenger side rear dual wheels where most of the pedestrian fatalities have occurred to provide something like the old railroad cow scoop or buffalo barrier--only in this instance the OEM directs the pedestrian collision away and out from under the bus when struck by this "scoop." I have not found the OEM of this new device to see what data is available about the efficacy of this device but anything that will prevent a "Crush" is something we must all consider. Dr. Ray Turner and

Douglas Carnall, @juliuzbeezer said...

I guess the key study your search missed is Leaf and Preusser's 1999 literature review: which concludes that the risk of death and injury does indeed rise with the speed of the colliding vehicle.
Those of us fortunate enough to have had a basic scientific education find this an unsurprising result: the kinetic energy of a moving object increases with the square of its velocity. The more energy imparted to the body in the event of a collision, the greater the damage.

David Friedman said...


I think the question being discussed is not whether the risk rises with the speed but how rapidly it rises.

Douglas Carnall, @juliuzbeezer said...

With the square of the velocity.

Ek = 1/2 * m * v^2

So at notional velocities (speeds) of 20 units, 30 units, and 40 units, the kinetic energy of the vehicle (which has to go somewhere if there is a collision) is (20*20)=400 units, (30*30)=900 units, (40*40)=1600 units.

So, if you double the speed (from 20 to 40), you quadruple the energy.

This physical law also explains why even quite modest reductions in speed limits leads to such a worthwhile reductions in fuel consumption.

Anonymous said...

Like anything you have to choose a trustworthy source. As much as we mistrust the government, their analysis is pretty solid. My brother is marine biologist for the government and we've discussed the "most probable result" when he prepares reports. Avoid bias in either direction, either toward harvesters or environmentalists. Don't get me wrong - I don't trust everything in every government report. It appears the exaggerated numbers are from a UK government source. However what appears to be a trustworthy "US gov" source for this info is In this report fatality rate is 3.7% for 21-25 mph, 12.5% for 31-35 mph, and 36.1% for 46+ mph. It appears Ashton and Mackay have an axe to grind and are biased. BTW & PS - One of the largest myths in history is that Columbus' sailors believed the world was flat.